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The broadcaster was diagnosed with mouth and throat cancer last year but has now revealed the good news via Twitter.
Baker posted: "The call I have been waiting for just happened. Turns out I won. I'm all clear. I'm well again."
He added: "I will be wearing this hat for the foreseeable future," along with a photo of himself sporting a baseball cap that bears the word "Lucky".
Baker had previously spoken about his diagnosis with The Guardian at the weekend, saying: "I'm not queasy about it, I just don't find it an interesting subject. It bores me, to tell the truth. Some people enjoy talking about grim situations. I never have. Treat it like a roundabout and drive straight on."
The broadcaster added: "You know, I've had tremendous fun for the last 30 years. It is an enormously absurd way to earn a living, and you can never lose sight of that.
"And when you get cancer for eight months, it's a drag, but all you want to do is get back to the goofy wonderland in which you rattle around. Yes, this got in the way for a while, but let's not dwell on that."
Baker had previously said that returning to his BBC London radio show was like "turning a corner" in his fight against cancer.
View a gallery of Danny Baker's career in pictures below:
